Blender 2.8 - Cloths Don't Follow Armature In Pose Mode or They Shift Positions
I've tried to correct with the method explained below, if it still doesn't work, try with the Mesh Deform method as explained here.

Deactivate the Armature modifier visibility (screen icon button) for both the arm and the straps, so that the armature doesn't move the one or the other:



Then you can see that arm and straps are not aligned, and the object even go through each other, you need to correct this in Object mode and in Edit mode.




Once you're good, in the strap's Data Transfer modifier, click on Vertex Data, on Vertex Group(s), Generate Data Layers and Apply:



Reactivate the armature visibility for both arm and straps, move the bones, it works, even though it will probably need some adjustments: